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Princess Poly claims that the equation (3x−4i)(7x−8)(3x+4i)=0 has three roots, a real root and a complex root with a multiplicit

Serjik [45]

Given equation:

$(3x-4i)(7x-8)(3x+4i)=0$

i.e., $3x-4i=0$ and $7x-8=0$ and $3x+4i=0$

i.e., $3x=4i$ and $7x=8$ and $3x=-4i$

i.e., $x=\frac{4i}{3}$ and $x=\frac{8}{7}$ and $x=-\frac{4i}{3}$

Therefore, the given equation has a real root i.e., $x=\frac{8}{7}$

and two complex conjugate roots i.e., $x=\frac{4i}{3}$ and $x=-\frac{4i}{3}$

Hence, option C is correct.

4 0

3 years ago

Which of the following describes the sum in terms of p and q?(1 point)

snow_tiger [21]

The description of the summation expression given as p + (-q) is the sum, p + (-q), is the number located a distance, |p|, from , q, in the negative direction.

<h3>How to describe the sum in terms of p and q?</h3>

The summation expression is given as:

p + (-q)

In the above summation expression, we assume that:

p ⇒ Positive number

- q ⇒ Negative number

Having said that:

The expression -q would go in the negative direction if plotted on a number line

This means that the description of the summation expression given as p + (-q) is the sum, p + (-q), is the number located a distance, |p|, from , q, in the negative direction.

Hence, the description of the summation expression given as p + (-q) is the sum, p + (-q), is the number located a distance, |p|, from , q, in the negative direction.

Read more about expressions at:

brainly.com/question/723406

#SPJ1

6 0

2 years ago

When you subtract 8from 10 what is the different

Alinara [238K]

Answer:

2

Step-by-step explanation:

Difference = 10 - 8 = 2

Hope it helps you in your learning process.

8 0

3 years ago

1. Find the 90% Cl for the population mean if sample

Elden [556K]

Answer:

The answer is below

Step-by-step explanation:

1)

mean (μ) = 12, SD(σ) = 2.3, sample size (n) = 65

Given that the confidence level (c) = 90% = 0.9

α = 1 - c = 0.1

α/2 = 0.05

The z score of α/2 is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.65

The margin of error (E) is given as:

$E=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} } =1.65*\frac{2.3}{\sqrt{65} } =0.47$

The confidence interval = μ ± E = 12 ± 0.47 = (11.53, 12.47)

2)

mean (μ) = 23, SD(σ) = 12, sample size (n) = 45

Given that the confidence level (c) = 88% = 0.88

α = 1 - c = 0.12

α/2 = 0.06

The z score of α/2 is the same as the z score of 0.44 (0.5 - 0.06) which is equal to 1.56

The margin of error (E) is given as:

$E=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} } =1.56*\frac{12}{\sqrt{45} } =2.8$

The confidence interval = μ ± E = 23 ± 2.8 = (22.2, 25.8)

8 0

3 years ago

Derivative of<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B3x%7D%5E%7B2%7D%20-%202x%20-%201%20%7D%7B%20%7Bx%7D%5E%7B2

Anastaziya [24]

Answer:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

Step-by-step explanation:

we would like to figure out the derivative of the following:

$\displaystyle \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

to do so, let,

$\displaystyle y = \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

By simplifying we acquire:

$\displaystyle y = 3 - \frac{2}{x} - \frac{1}{ {x}^{2} }$

use law of exponent which yields:

$\displaystyle y = 3 - 2 {x}^{ - 1} - { {x}^{ - 2} }$

take derivative in both sides:

$\displaystyle \frac{dy}{dx} = \frac{d}{dx} (3 - 2 {x}^{ - 1} - { {x}^{ - 2} } )$

use sum derivation rule which yields:

$\rm\displaystyle \frac{dy}{dx} = \frac{d}{dx} 3 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

By constant derivation we acquire:

$\rm\displaystyle \frac{dy}{dx} = 0 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

use exponent rule of derivation which yields:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ - 1 -1} ) - ( - 2 {x}^{ - 2 - 1} )$

simplify exponent:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ -2} ) - ( - 2 {x}^{ - 3} )$

two negatives make positive so,

$\displaystyle \frac{dy}{dx} = 2 {x}^{ -2} + 2 {x}^{ - 3}$

<h3>further simplification if needed:</h3>

by law of exponent we acquire:

$\displaystyle \frac{dy}{dx} = \frac{2 }{x^2}+ \frac{2}{x^3}$

simplify addition:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

and we are done!

5 0

3 years ago